Filter felt damp ???? I don't know why the filter is getting wet. Is there a humidifier on the return air that is leaking? Lack of air through the furnace will definitely cause the limit switch to open and can be caused from a dirty filter certainly, or a lot of dirt in the blower wheel. Also if this furnace has cooling then it has a coil above the furnace ( if it's an upflow furnace) and if this coil has an excessive amount of dirt on the INSIDE portion of the coil that will restrict air flow . So you need to check these items.

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